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\chapter{Topology}
\begin{definition}[Base of Topology]
\noindent Let $(X,\tau)$ be a topological space, $B\subseteq \tau$, a collection of open subsets of $X$. If elements of $B$ cover open subsets of $X$, then $B$ is called a base for the topology $\tau$.
\end{definition}
\begin{lemma}
\noindent Let $X$ be a non-empty set, $B$ a collection of subsets of $X$. If elements of $B$ cover $X$, and cover finite intersections of its elements, then the collection of arbitrary unions of elements of $B$ forms a topology on $X$, and $B$ forms a base for this topology.
\end{lemma}
natural example of connected but not bath connected?
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